Calculating Simple Interest with a Half-Yearly Rate

This problem involves calculating the total amount Somu needs to pay back on a loan taken at a simple interest rate specified on a half-yearly basis.

Understanding the Given Information

• Principal amount (P) = ₹10,000
• Simple Interest Rate = 7% half yearly
• Time period (T) = 3 years

The key here is the interest rate being "7% half yearly". Simple interest is typically calculated using a yearly rate. A rate of 7% half yearly means that interest is calculated at 7% for every six-month period. Over a full year, this would be 7% + 7% = 14% per year.

Converting Half-Yearly Rate to Yearly Rate

Since the simple interest formula uses a yearly rate, we convert the given half-yearly rate:

Yearly Interest Rate (R) = Rate per half year $\times$ Number of half years in a year

Yearly Interest Rate (R) = 7% $\times$ 2 = 14% per annum.

Calculating Simple Interest

The formula for Simple Interest (SI) is:

$$SI = \frac{P \times R \times T}{100}$$

Where:

• P = Principal amount
• R = Yearly Interest Rate
• T = Time in years

Let's substitute the values:

$$SI = \frac{10000 \times 14 \times 3}{100}$$

$$SI = \frac{10000 \times 42}{100}$$

$$SI = 100 \times 42$$

$$SI = 4200$$

So, the simple interest accrued over 3 years is ₹4,200.

Calculating the Total Amount Paid Back

The total amount Somu will pay back is the sum of the principal amount and the simple interest.

Total Amount = Principal + Simple Interest

Total Amount = ₹10,000 + ₹4,200

Total Amount = ₹14,200

Thus, Somu will pay ₹14,200 to the money lender after 3 years.

Revision Table: Key Simple Interest Concepts

Additional Information on Simple Interest and Rates

Simple interest is a straightforward way to calculate the interest on a loan or investment. Unlike compound interest, simple interest is only earned or charged on the initial principal amount throughout the entire time period.

When dealing with interest rates, it's crucial to align the time unit of the rate with the time unit used for the total duration. In this problem, the rate was given per half-year, but the time was given in years. We converted the rate to a yearly rate (per annum) to use it directly in the standard simple interest formula where Time (T) is in years.

Alternatively, one could adjust the time period. If the rate is 7% per half-year, then 3 years is equal to 6 half-year periods. The formula could be used as:

$$SI = \frac{P \times (\text{Rate per period}) \times (\text{Number of periods})}{100}$$

$$SI = \frac{10000 \times 7 \times 6}{100}$$

$$SI = \frac{10000 \times 42}{100}$$

$$SI = 4200$$

This confirms that both methods yield the same simple interest amount, leading to the same total amount to be paid back.